bidirectional arrows between latent and observed variables?

[julia...@gmail.com]

Hi everyone,
I'm new to lavaan and SEM. A quick question about the structure of my model (see attached). Can a latent variable simultaneously influence and be influenced by an observed variable? In other words, do the bidirectional arrows on paths a, c, and f make sense, or do they need to be unidirectional?

Option A (bidirectional arrows):
Under latent variables I have ξ1=~x1+x2+x3+x4 and under regressions I have ξ1~x5+x6+x9

Option B (unidirectional arrows):
Under latent variables I have ξ1=~x1+x2+x3+x4 and under regressions I have ξ1~1

Thanks for your help!

[Terrence Jorgensen]

Bidirectional (two-headed) arrows represent covariances/correlations, not regressions.  There are scripted with double-tildes

ξ1 ~~ x5 + x6 + x9

If you actually want to model regressions in both directions, your model will not be identified unless you constrain those paths (e.g., to equality, or proportionally equal):

ξ1 ~ a*x5 + b*x6 + c*x9

x5 ~ a*ξ1

x6 ~ b*ξ1

x9 ~ c*ξ1

Terry

[Mikko Rönkkö]

Hi

Model identification for bidirectional paths does not generally require fixing the proportion of the directions. Here is an example of an identified model:

library(lavaan)

set.seed(2)

MODEL <- "

Xa =~ x1 + x2 + x3 + x4

Xb =~ x5 + x6 + x7 + x8

Xa ~ x1 + Xb

"

data <- simulateData(MODEL)

fit <- sem(MODEL, data)

summary(fit)

The model in the figure attached to the original email, however, is almost certainly not identified. 

Mikko

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